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NTA Abhyas JEE Main2020MathematicsVector AlgebraPractice

If a → and b → are unit vectors making an angle α with each other, such that α ∈ 0 , π and a → + 2 b → < 5 , then α lies in the interval

Options

A0 , π
B0 , π 2
Cπ 2 , 2 π 3
Dπ 6 , 5 π 6

Correct answer

A. 0 , π

Step-by-step solution

a → + 2 b → < 5 ⇒ a → + 2 b → 2 < 25 ⇒ a → 2 + 4 b → 2 + 4 a → ⋅ b → < 25 ⇒ 1 + 4 + 4 cos ⁡ α < 25 ⇒ cos ⁡ α < 5 ⇒ α ∈ 0 , π

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